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Intern  Joined: 27 Sep 2011
Posts: 13
What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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1
6 00:00

Difficulty:   5% (low)

Question Stats: 78% (00:54) correct 22% (01:06) wrong based on 233 sessions

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What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60
Manager  Joined: 21 Aug 2010
Posts: 161
Location: United States
GMAT 1: 700 Q49 V35
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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2
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

Posted from my mobile device
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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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3
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 27 Sep 2011
Posts: 13
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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VeritasPrepKarishma wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.

Thank you very much.......... I am very weak in this type of PS math Could you please explain 12! math you have given ?
Manager  Joined: 21 Aug 2010
Posts: 161
Location: United States
GMAT 1: 700 Q49 V35
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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VeritasPrepKarishma wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.

n = 10

I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12

Do you have any faster method which can be used for bigger factorials?
_________________
-------------------------------------
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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2
Check out this post: http://www.veritasprep.com/blog/2011/06 ... actorials/

It discusses how to solve such questions quickly.
_________________
Karishma
Veritas Prep GMAT Instructor

Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Similar question to practice: what-is-the-largest-integer-n-such-that-2-n-is-a-factor-of-158297.html
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Current Student D
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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Nice One.
Here breaking down 12^10 => 2^20 *3^10
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EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
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GMAT 1: 800 Q51 V49
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

GMAT assassins aren't born, they're made,
Rich
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Non-Human User Joined: 09 Sep 2013
Posts: 14017
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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_________________ Re: What is greatest positive integer n such that 2^n is a factor of 12^10   [#permalink] 21 Jul 2019, 05:42
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